{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FA4WFF4RBHGKZHY3OSMTH7IIFB","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"3a4757513d0950c1468a9aa7d93894752c3fdf7ea980e69f9c482577c9b47495","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-07-05T19:07:59Z","title_canon_sha256":"b1bea1a8f62a236e6a00c11cbd773087f334d0bf340bd455c6ae58c4d7b5cf40"},"schema_version":"1.0","source":{"id":"1607.01368","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.01368","created_at":"2026-05-18T01:11:27Z"},{"alias_kind":"arxiv_version","alias_value":"1607.01368v1","created_at":"2026-05-18T01:11:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.01368","created_at":"2026-05-18T01:11:27Z"},{"alias_kind":"pith_short_12","alias_value":"FA4WFF4RBHGK","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FA4WFF4RBHGKZHY3","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FA4WFF4R","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:c2aba5c2ae4301767a4b2ffb14277974a8ac80b2abedcfa6559dd0c65913b8b1","target":"graph","created_at":"2026-05-18T01:11:27Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study cyclic codes with arbitrary length over Fp+vFp where theta(v)=av, a in Fp and v^2=0. We characterize all existing codes in case of O(theta)|n by using certain projections from (Fp+vFp)[x;theta] to Fp[x]. We provide an explicit expression for the ensemble of all possible codes. We also prove useful properties of these codes in the case where O(theta)|n does not hold. We provide results and examples to illustrate how the codes are constructed and how their encoding and decoding are realized.","authors_text":"Javad Haghighat, Reza Dastbasteh, Seyyed Hamed Mousavi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-07-05T19:07:59Z","title":"Characterization of the skew cyclic codes over Fp+vFp"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01368","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:fe5c338da5ab650df9c57b7f3a7c0450d42d4ea1253e4ec1836db247147d6127","target":"record","created_at":"2026-05-18T01:11:27Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"3a4757513d0950c1468a9aa7d93894752c3fdf7ea980e69f9c482577c9b47495","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-07-05T19:07:59Z","title_canon_sha256":"b1bea1a8f62a236e6a00c11cbd773087f334d0bf340bd455c6ae58c4d7b5cf40"},"schema_version":"1.0","source":{"id":"1607.01368","kind":"arxiv","version":1}},"canonical_sha256":"283962979109ccac9f1b749933fd082853ce79ff20c038722580f7bbbb5615a7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"283962979109ccac9f1b749933fd082853ce79ff20c038722580f7bbbb5615a7","first_computed_at":"2026-05-18T01:11:27.980454Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:27.980454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lRQ+9LtcuaNLtXzcjbgRtezEtMYB94LA3WEV9DjJZjbH9WICisgT68j+F9eRvwPcF86Yr6wu+SfvjGEQZ5lXBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:27.980953Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.01368","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe5c338da5ab650df9c57b7f3a7c0450d42d4ea1253e4ec1836db247147d6127","sha256:c2aba5c2ae4301767a4b2ffb14277974a8ac80b2abedcfa6559dd0c65913b8b1"],"state_sha256":"1f4d84551c91a07408d6a98cd0f386170f1ccdf130c6d04204b6161d6fd83cac"}